A proof that $\mathcal {C}^2$ and $\mathcal {T}^2$ are distinct measures
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- by Lawrence R. Ernst PDF
- Trans. Amer. Math. Soc. 173 (1972), 501-508 Request permission
Abstract:
We prove that there exists a nonempty family $X$ of subsets of ${{\text {R}}^3}$ such that the two-dimensional Carathéodory measure of each member of $X$ is less than its two-dimensional $\mathcal {T}$ measure. Every member of $X$ is the Cartesian product of 3 copies of a suitable Cantor type subset of ${\text {R}}$.References
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 173 (1972), 501-508
- MSC: Primary 28A10
- DOI: https://doi.org/10.1090/S0002-9947-1972-0310164-3
- MathSciNet review: 0310164